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      Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases

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          Abstract

          Alkaline-earth and ytterbium cold atomic gases make it possible to simulate SU(N)-symmetric fermionic systems in a very controlled fashion. Such a high symmetry is expected to give rise to a variety of novel phenomena ranging from molecular Luttinger liquids to (symmetry- protected) topological phases. We review some of the phases that can be stabilized in a one dimensional lattice. The physics of this multicomponent Fermi gas turns out to be much richer and more exotic than in the standard SU(2) case. For N > 2, the phase diagram is quite rich already in the case of the single-band model, including a molecular Luttinger liquid (with dominant superfluid instability in the N-particle channel) for incommensurate fillings, as well as various Mott-insulating phases occurring at commensurate fillings. Particular attention will be paid to the cases with additional orbital degree of freedom (which is accessible experimentally either by taking into account two atomic states or by putting atoms in the p-band levels). We introduce two microscopic models which are relevant for these cases and discuss their symmetries and strong coupling limits. More intriguing phase diagrams are then presented including, for instance, symmetry protected topological phases characterized by non-trivial edge states.

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          Journal
          2015-09-15
          2016-02-28
          10.1016/j.aop.2016.01.011
          1509.04597

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Ann.Phys. 367, 50 (2016)
          59 pages, 20 figures. Review article published in Annals of Physics. Some minor errors fixed
          cond-mat.quant-gas

          Quantum gases & Cold atoms

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